I have an IMTU Terran Confederation which is considered to 'own' space everywhere else but Terra itself- an outgrowth of the Outer Space Treaty.
https://en.wikipedia.org/wiki/Outer_Space_Treaty
The treaty has been altered to allow for national ships to be armed, largely as a result of piracy, but warships are all nominally under the flag of the Terran Confederation and are to be called to international service in the event of war with extra-Confederation humans or hostile aliens.
As such, the starports are technically just a facility supporting a world that is TC territory.
However, areas on planets are colonized by TC charters, effectively development agreements awarded to nations, and for all intents and purposes within the borders of the colony it is an extension of national soil, even though technically the charter can be pulled or run out and not extended.
To complicate matters, the TC worlds with several chartered colonies have found a need to decide on world issues together, with people growing up on a world having more allegiance and identity with that world then their originating nations. This trend is causing social, political and economic tensions.
So a TC world often has elements of a Captive Government, a Balkanized world and a Participatory or Representative Democracy.
As such, the starport is considered TC territory and operates by TC rules and governance, but may have to deal or negotiate regarding world council issue, particularly BioQuarantine measures and an agreed upon law level re: import of weapons.
Often, the most restrictive nation/colony will get it's restrictions on weapons imports honored at the starport, even though there may be much more relaxed law level polities on-planet.
Nations may operate their own spaceports for in-system activity, usually for raw material mining and gas refining or landing 'domestic' produced goods in orbiting facilities, but there must always be a TC customs check, to keep the peace AND pay for the TC.
The Confederation is largely bankrolled through port fees, colony charter auctions, pharmabank actitivies, and import/export tariffs, which suits the member nations fine as it keeps the TC on a fiscal leash, focused on playing ball with starport access AND improving trade/economic activity, and avoids the politics of taxation that would ensue if a proportionate or 'TC citizen' or income tax was enacted.